Related papers: Towards the Derived Jacquet-Emerton Module Functor

Let $G_n$ be an inner form of a general linear group over a non-Archimedean field. We fix an arbitrary irreducible representation $\sigma$ of $G_n$. Lapid-M\'inguez give a combinatorial criteria for the irreducibility of parabolic induction…

Let $\mathrm{F}$ be a local non-archimedean field of residue characteristic $p$ and $\overline{\mathbb{F}}_\ell$ an algebraic closure of a finite field of characteristic $\ell \neq p$. We extend the results of Lapid and M\'inguez concerning…

Let $G$ be a $p$-adic group that splits over an unramified extension. We decompose $Rep_{\Lambda}^{0}(G)$, the abelian category of smooth level $0$ representations of $G$ with coefficients in $\Lambda=\overline{\mathbb{Q}}_{\ell}$ or…

Let $G$ be a connected reductive group over a perfect field $k$. We study a certain normal reductive monoid $\overline M$ associated to a parabolic $k$-subgroup $P$ of $G$. The group of units of $\overline M$ is the Levi factor $M$ of $P$.…

Let G be the group of rational points of a reductive connected group over a finite field (resp. nonarchimedean local field of characteristic p) and R a commutative ring. The unipotent (resp. pro-p Iwahori) invariant functor takes a smooth…

The Geometrical Lemma is a classical result in the theory of (complex) smooth representations of $p$-adic reductive groups, which helps to analyze the parabolic restriction of a parabolically induced representation by providing a filtration…

Let $G_{n}=\operatorname{GL}_{n}(F)$, where $F$ is a non-archimedean local field with residue characteristic $p$ and where $n=2k$ is even. In this article, we investigate a question occurring in the decomposition of the category of…

We analyze reducibility points of representations of $p$-adic groups of classical type, induced from generic supercuspidal representations of maximal Levi subgroups, both on and off the unitary axis. We are able to give general, uniform…

The notion of relative cuspidality for distinguished representations attached to $p$-adic symmetric spaces is introduced. A characterization of relative cuspidality in terms of Jacquet modules is given and a generalization of Jacquet's…

We study the category $\mathcal{F}_n$ of finite-dimensional integrable representations of the periplectic Lie superalgebra $\mathfrak{p}(n)$. We define an action of the Temperley--Lieb algebra with infinitely many generators and defining…

Let $H$ be the fixed point group of a rational involution $\si$ of a reductive $p$-adic group of charactersistic different from 2(this new version allows to remove the hypothesis on the characteristic of the residue field, see Proposition…

Let $F$ be a nonarchimedean local field with residue field of cardinality $q$, let $G$ be the $F$-points of a connected reductive group defined over $F$, let $P$ and $Q$ be two parabolic subgroups with the same Levi factor $M$. We construct…

In this paper we define a functor from the algebraic category of frontal Hilbert algebras to the algebraic category of frontal implicative semilattices which is left adjoint to the forgetful functor from the category of frontal implicative…

We introduce a derived smooth duality functor on the unbounded derived category of smooth mod p representations of a p-adic Lie group. Using this functor we relate various subcategories of admissible complexes.

We propose the notion of the {\em crystalline sub-representation functor} defined on $p$-adic representations of the Galois groups of finite extensions of $\Qp$, with certain restrictions in the case of integral representations. By studying…

We construct a tensor functor from the category of super representations of the superlinear group Gl(m,n) over a field of characteristic zero to the category of super representations of the linear group Gl(m-n) over some extension field…

Let $\Delta$ be a closed, cocompact subgroup of $G \times \widehat{G}$, where $G$ is a second countable, locally compact abelian group. Using localization of Hilbert $C^*$-modules, we show that the Heisenberg module…

Let $p$ be a prime number and $\Bbbk=\bar{\mathbb{F}}_p$, the algebraic closure of the finite field $\mathbb{F}_p$ of $p$ elements. Let ${\bf G}$ be a connected reductive group defined over $\mathbb{F}_p$ and ${\bf B}$ be a Borel subgroup…

We extend the theory of local constants to l-adic families of representations of GL_n(F) where F is a p-adic field with l not equal to p. We construct zeta integrals and gamma factors for representations coming from the conjectural "local…

Let $G$ be the group of rational points of a split connected reductive group over a non-archimedean local field of residue characteristic $p$, and let $\mathcal{H}$ denote the pro-$p$ Iwahori-Hecke algebra of $G$ over a field of…